**By Serge Lang,**

__A First Course in Calculus__

The purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica tions which accompany them The very talented students, with an ob vious aptitude for mathematics, will rapidly require a course in functions of one real variable, or less as it is understood by professional is not primThe purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica tions which accompany them The very talented students, with an ob vious aptitude for mathematics, will rapidly require a course in functions of one real variable, or less as it is understood by professional is not primarily addressed to them although mathematicians This book I hope they will be able to acquire from it a good introduction at an early age I have not written this course in the style I would use for an advanced monograph, on sophisticated topics One writes an advanced monograph for oneself, because one wants to give permanent form to one s vision of some beautiful part of mathematics, not otherwise ac cessible, somewhat in the manner of a composer setting down his sym phony in musical notation This book is written for the students to give them an immediate, and pleasant, access to the subject I hope that I have struck a proper com promise, between dwelling too much on special details and not giving enough technical exercises, necessary to acquire the desired familiarity with the subject In any case, certain routine habits of sophisticated mathematicians are unsuitable for a first course Rigor This does not mean that so called rigor has to be abandoned.

This was an excellent text for self studying the beginnings of calculus It makes proofs accessible, and even taught me how to prove concepts that seemed obvious but were easy to forget when not used for a while Learning how to derive and prove concepts like this is essential for someone who wants to study physics, which is the case for me.I have reservations for recommending this book for Calculus II and beyond Seeing second and third semester calculus topics listed in the table of contents rais [...]

Loved it Short refresher on calculus without being too breif I didn t finish the entire book I got up to power series but will come back to it later I need something with theory and practice for now A lot of steps get skipped later in the text so you should have a solid algebraic background.

This is a very good book for Calculus beginners The new edition of the book has fully solved examples.